The body of the spacecraft weighs 322 lb on earth and has a radius of gyration about its $z$ -axis of 1.5 ft. Each of the two solar panels may be treated as a uniform flat plate weighing 16.1 lb. If the spacecraft is rotating about its $z$ -axis at the angular rate of 1.0 rad/sec with $\theta=0,$ determine the angular rate $\omega$ after the panels are rotated to the position $\theta=\pi / 2$ by an internal mechanism. Neglect the small momentum change of the body about the $y$ -axis.